We need to know a little bit more about you. Budget, skiing skill level, winter driving skills (or lack thereof), what things you like (e.g. powder vs groomers), lesson needs, terrain park needs, crowds+tourists vs small homey and locals, what time of year you are planning for, etc.
In general, the park city triumverant (PC, Deer Valley and the Canyons) get slightly less snow than the Cottonwod canyons quad (Alta, Snowbird, Brighton and Solitude). Because the PC base areas are relatively flat, navigation is easier. Just getting to the CC quad can be an adventure. There are more things to do in the villages on the PC side, but it's easier to have family time (not likely with your teenagers!?) if you stay in the small places at the base village in Alta. On the canyon side, it's easy and CHEAP to stay in town (20 minute drive UP the canyons to get to the resorts) and there are plenty of "city" things to do at night.
All the resorts have roughly similar terrain. Deer Valley is know for it's excellent grooming, but slightly less challenging terrain. Oh - and their food is outstanding and quite expensive. Snowbird is known for its it's tram and excellent terrain. Alta is more of throwback to skiing history (Alta and Deer Valley do not allow snowboards). The Canyons used to be more of a place for local snowboarders but that's changed with the terrain expansion. Solitude and Brighton are smaller, cosier and have a higher percentage of locals to tourists. Park City has the world wide rep. PC has plenty of challenging terrain plus tons of cruisers.
If you're not much for travelling around, I'd spend each day at different resort in either the Park City area or the Cottonwood canyons area.